The standard approach to managing chronic lymphocytic leukemia (CLL) and small lymphocytic leukemia (SLL) is to wait until you have symptoms before treatment is given.

The goal of this clinical research study is to learn if providing earlier treatment for CLL or SLL with ibrutinib in patients who do not have symptoms will be more effective than waiting until symptoms develop.

This is an investigational study. Ibrutinib is FDA approved and commercially available for the treatment of patients with CLL or SLL. It is considered investigational to give ibrutinib to CLL and SLL patients before symptoms develop.

The study doctor can describe how the study drug is designed to work.

Up to 50 participants will be enrolled in this study. All will take part at MD Anderson.

Study Drug Administration:

If you are found to be eligible to take part in this study, you will take ibrutinib by mouth 1 time every day. Each dose should be taken with about 1 cup (8 ounces) of water.

If you miss a dose of ibrutinib, it can be taken as soon as possible on the same day. You should take your next dose as scheduled. If you forget to take a dose, do not take extra capsules on the next day to "make up" the missed dose.

You will be given standard drugs, such as allopurinol or valacyclovir, to help decrease the risk of side effects. You may ask the study staff for information about how the drugs are given and their risks. If you have side effects, your dose of ibrutinib may be lowered or temporarily stopped until you recover from the side effects.

Length of Treatment:

You may take ibrutinib for up to 2 years (24 cycles). If at the end of 2 years you are benefitting from ibrutinib and the study doctor thinks it is in your best interest to continue taking it, other treatment options will be discussed with you to allow you to continue to take ibrutinib.

You will no longer be able to take the study drug if the disease gets worse, if intolerable side effects occur, or if you are unable to follow study directions.

Study Visits:

Each cycle is 28 days.

On Day 28 of Cycles 1-3 and then every 3 cycles after that until Cycle 24 (Cycles 6, 9, 12, and so on):

• Blood (about 2 tablespoons) will be drawn for routine tests.
• You will have a physical exam.
• You will have an EKG.

On Day 28 of Cycles 1, 3, 6, 12, and 24, blood (about 3 tablespoons) will be drawn to test for genetic mutations related to the disease. At Months 3, 6, and 12, additional blood (about 8 teaspoons) will be drawn for immune system testing.

On Day 28 of Cycles 6, 12, 18 and 24, you will have CT, MRI or PET/CT scan to check the status of the disease. Depending on the results of the CT, MRI or PET/CT scans, you may not need to have these scans repeated. The doctor will discuss this with you.

On Day 28 of Cycles 6, 12 and 24, you will have a bone marrow biopsy to check the status of the disease.

If the doctor thinks it is needed or if the disease gets worse, some tests/procedures, such as physical exams and blood draws for routine tests, may be repeated more often.

Long-term follow-up:

Every 3 months, during a regularly scheduled clinic visit (if you are still receiving care at MD Anderson) or by phone (if you are receiving care outside of MD Anderson), you will be asked how you are doing, if you are still taking ibrutinib, and if you have any side effects. If called, this call should last about 5-10 minutes.

Inclusion Criteria:

1. Patients must be age >/=18 years at the time of informed consent, understand and voluntarily sign an informed consent, and be able to comply with study procedures and follow-up examinations.
2. No treatment indication according to IWCLL/NCI-WG (International Working Group in Chronic Lymphocytic Leukemia/National Cancer Institute-Working Group) 2008 criteria
3. Estimated time to first treatment of 3 years or less according to MDACC nomogram
4. ECOG performance status of 0-2
5. Male and female subjects who agree to use both a highly effective method of birth control (eg, implants, injectables, combined oral contraceptives, some intrauterine devices [IUDs], complete abstinence , or sterilized partner) and a barrier method (eg., condoms, vaginal ring, sponge, etc) during the period of therapy and for 30 days after the last dose of study drug for females and 90 days for males. OR Female subjects who are of non-reproductive potential (ie, post-menopausal by history - no menses for >/=1 year; OR history of hysterectomy; OR history of bilateral tubal ligation; OR history of bilateral oophorectomy)
6. Adequate hepatic and renal function as indicated by all of the following: Total bilirubin </=1.5 x institutional Upper Limit of Normal (ULN) except for patients with bilirubin elevation due to Gilbert's disease or of non-hepatic origin who will be allowed to participate, provided bilirubin is </=3 x institutional ULN; an ALT </=2.5 x ULN; and estimated creatinine clearance (CrCl) of > 30 mL/min, as calculated by the Cockcroft- Gault equation.
7. PT/INR <1.5 x ULN and PTT (aPTT) <1.5 x ULN (unless abnormalities are unrelated to coagulopathy or bleeding disorder).
8. Free of prior malignancies for 3 years with exception of patients diagnosed with basal cell or non-metastatic squamous cell carcinoma of the skin, or carcinoma in situ of the cervix or breast, who are eligible even if they are currently treated or were treated and/or diagnosed in the past 3 years prior to study enrolment
9. Diagnosis of CLL/SLL that meets IWCLL diagnostic criteria

Exclusion Criteria:

1. Receipt of any prior therapy for CLL. Patients who have received "early intervention" with INVAC-1 vaccine against hTERT will be eligible provided all of the following exist: i) They had no response to the vaccine treatment (persistent CLL >1% in bone marrow). ii) ≥3 months have elapsed since the last dose of vaccine. iii) No residual toxicities attributable to the vaccine exist at the time of study enrollment. iv) The patient does not meet IWCLL criteria for requiring treatment.
2. Richter Transformation
3. Active malignancy requiring systemic therapy, other than CLL, with the exception of: adequately treated in situ carcinoma of the cervix uteri; adequately treated basal cell carcinoma or localized squamous cell carcinoma of the skin; previous malignancy confined and surgically resected (or treated with other modalities) with curative intent.
4. Systemic anticoagulation with warfarin or other Vitamin K antagonists
5. Active and uncontrolled autoimmune hemolytic anemia (AIHA) or autoimmune thrombocytopenia (ITP) requiring daily prednisone dose of >/=20 mg
6. Current and concurrent use of strong CYP3A4 inhibitors or inducers
7. Pregnant or breast-feeding females
8. Uncontrolled and active systemic fungal, bacterial, viral, or other infection (defined as exhibiting ongoing signs/symptoms related to the infection and without improvement, despite appropriate antibiotics or other treatment)
9. Any other severe concurrent disease, or history of serious organ dysfunction or disease involving the heart, kidney, liver or other organ system that, in the investigator's opinion, may place the patient at undue risk to undergo therapy with ibrutinib
10. Currently active, clinically significant cardiovascular disease, such as uncontrolled arrhythmia or Class 3 or 4 congestive heart failure as defined by the New York Heart Association Functional Classification; or a history of myocardial infarction, unstable angina, or acute coronary syndrome within 6 months prior to randomization
11. History of ischemic stroke within 6 months prior to enrollment
12. Evidence of bleeding diathesis or coagulopathy within 3 months (eg, von Willebrand's disease or hemophilia
13. Any history of symptomatic intracranial hemorrhage
14. Major surgical procedure with 4 weeks of first dose of study drug; open biopsy, or significant traumatic injury within 7 days prior to enrollment date; anticipation of need for major surgical procedure during the course of the study
15. Minor surgical procedures, fine needle aspirations or core biopsies within 3 days prior to enrollment date. Bone marrow aspiration and/or biopsy are allowed
16. Serious, non-healing wound, ulcer, or bone fracture
17. Vaccinated with live, attenuated vaccines within 4 weeks of first dose of study drug
18. Active, uncontrolled infection
19. Known history of human immunodeficiency virus (HIV) or active with hepatitis C virus (HCV) or hepatitis B virus (HBV). Subjects who are positive for hepatitis B core antibody, hepatitis B surface antigen, or hepatitis C antibody must have a negative polymerase chain reaction (PCR) result before enrollment. Those who are PCR positive will be excluded
20. Currently active, clinically significant hepatic impairment Child-Pugh class B or C according to the Child Pugh classification (see Appendix L)

through 24 months